This work reports results of numerical simulations of viscous incompressible flow past a sphere. The primary objective is to identify transitions that occur with increasing Reynolds number, as well as their underlying physical mechanisms. The numerical method used is a mixed spectral element/Fourier spectral method developed for applications involving both Cartesian and cylindrical coordinates. In cylindrical coordinates, a formulation, based on special Jacobi-type polynomials, is used close to the axis of symmetry for the efficient treatment of the ‘pole’ problem. Spectral convergence and accuracy of the numerical formulation are verified. Many of the computations reported here were performed on parallel computers. It was found that the first transition of the flow past a sphere is a linear one and leads to a three-dimensional steady flow field with planar symmetry, i.e. it is of the ‘exchange of stability’ type, consistent with experimental observations on falling spheres and linear stability analysis results. The second transition leads to a single-frequency periodic flow with vortex shedding, which maintains the planar symmetry observed at lower Reynolds number. As the Reynolds number increases further, the planar symmetry is lost and the flow reaches a chaotic state. Small scales are first introduced in the flow by Kelvin–Helmholtz instability of the separating cylindrical shear layer; this shear layer instability is present even after the wake is rendered turbulent.

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The dynamics and multiple-cycle evolution of the incompressible flow induced by a moving piston through the open valve of a motored piston-cylinder assembly was investigated using direct numerical simulation. A spectral element solver, adapted for moving geometries using an Arbitrary Lagrange/Eulerian formulation, was employed. Eight cycles were simulated and the ensemble- and azimuthally-averaged data were found to be in good agreement with experimentally determined means and fluctuations at all measured points and times. During the first half of the intake stroke the flow field is dominated by the dynamics of the incoming jet and the vortex rings it creates. With decreasing piston speed a large central ring becomes the dominant flow feature until the top dead center. The flow field at the end of the previous cycle is found to have a dominant effect on the jet breakup and the vortex ring dynamics below the valve and on the observed significant cyclic variations. Based on statistical averaging, the evolution of the turbulent flow field during the first half of the intake stroke is dominated by the jet breakup process leading to a strongly anisotropic behavior. In the second part of the intake stroke, the decrease of the incoming jet velocity results in a more isotropic behavior.

The dynamics of fuel-lean (equivalence ratio φ = 0.5) premixed hydrogen/air atmospheric pressure flames are investigated in open cylindrical tubes with diameters of d = 1.0 and 1.5 mm using three-dimensional numerical simulations with detailed chemistry and transport. In both cases, the inflow velocity is varied over the range where the flames can be stabilized inside the computational domain. Three axisymmetric combustion modes are observed in the narrow tube: steady mild combustion, oscillatory ignition/extinction and steady flames as the inflow velocity is varied in the range 0.5 6 U IN 6 500 cm s −1 . In the wider tube, richer flame dynamics are observed in the form of steady mild combustion, oscillatory ignition/extinction, steady closed and open axisymmetric flames, steady non-axisymmetric flames and azimuthally spinning flames (0.5 6 U IN 6 600 cm s −1 ). Coexistence of the spinning and the axisymmetric modes is obtained over relatively wide ranges of U IN . Axisymmetric simulations are also performed in order to better understand the nature of the observed transitions in the wider tube. Fourier analysis during the transitions from the steady axisymmetric to the three-dimensional spinning mode and to the steady non-axisymmetric modes reveals that the m = 1 azimuthal mode plays a dominant role in the transitions.

We present three-dimensional direct numerical simulations (DNS) of the Kida vortex flow, a prototypical turbulent flow, using a novel high-order lattice Boltzmann (LB) model. Extensive comparisons of various global and local statistical quantities obtained with an incompressible-flow spectral element solver are reported. It is demonstrated that the LB method is a promising alternative for DNS as it quantitatively captures all the computed statistics of fluid turbulence.

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